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Algebra and Discrete Mathematics, 2019, том 27, выпуск 2, страницы 202–211
(Mi adm703)
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RESEARCH ARTICLE
The classification of serial posets with the non-negative quadratic Tits form being principal
Vitalij M. Bondarenkoa, Marina V. Styopochkinab a Institute of Mathematics, Tereshchenkivska str., 3, 01024 Kyiv, Ukraine
b Zhytomyr National Agroecological Univ., Staryi Boulevard, 7, 10008 Zhytomyr, Ukraine
Аннотация:
Using (introduced by the first author) the method of (min, max)-equivalence, we classify all serial principal posets, i.e. the posets $S$ satisfying the following conditions: (1) the quadratic Tits form $q_S(z)\colon\mathbb{Z}^{|S|+1}\to\mathbb{Z}$ of $S$ is non-negative; (2) $\operatorname{Ker}q_S(z):=\{t\mid q_S(t)=0\}$ is an infinite cyclic group (equivalently, the corank of the symmetric matrix of $q_S(z)$ is equal to $1$); (3) for any $m\in\mathbb{N}$, there is a poset $S(m)\supset S$ such that $S(m)$ satisfies (1), (2) and $|S(m)\setminus S|=m$.
Ключевые слова:
quiver, serial poset, principal poset, quadratic Tits form, semichain, minimax equivalence, one-side and two-side sums, minimax sum.
Поступила в редакцию: 14.03.2019
Образец цитирования:
Vitalij M. Bondarenko, Marina V. Styopochkina, “The classification of serial posets with the non-negative quadratic Tits form being principal”, Algebra Discrete Math., 27:2 (2019), 202–211
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm703 https://www.mathnet.ru/rus/adm/v27/i2/p202
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Страница аннотации: | 79 | PDF полного текста: | 113 | Список литературы: | 17 |
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